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Characteristic determinant approach to the spectrum of one-dimensional PT-symmetric systems

Vladimir Gasparian1,*, Peng Guo2,3,†, Antonio Pérez-Garrido4,‡, and Esther Jódar4,§

  • *Contact author: vgasparyan@csub.edu
  • †Contact author: peng.guo@dsu.edu
  • ‡Contact author: antonio.perez@upct.es
  • §Contact author: esther.jferrandez@upct.es
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Phys. Rev. Research 7, 033257 – Published 15 September, 2025

DOI: https://doi.org/10.1103/d9wj-v62g

Abstract

We obtain a closed-form expression for the energy spectrum of PT-symmetric superlattice systems with complex potentials of periodic sets of two δpotentials in the elementary cell. In the presence of periodic gain and loss, we analyzed in detail a diatomic crystal model, varying either the scatterer distances or the potential heights. It is shown that at a certain critical value of the imaginary part of the complex amplitude, topological states depending on the lattice size and the configuration of the unit cell can be pushed out from the given region. This may happen at the PT-symmetry breaking (exceptional) points.

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Phys. Rev. Research 7, 033257– Published 15 September, 2025
  • Received 26 March 2025
  • Accepted 29 August 2025
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